Distributed optimization of multi-integrator agent systems with mixed neighbor interactions

Abstract

In this paper, we consider a constrained distributed optimization problem for multi-integrator agent systems with mixed neighbor interactions, where the neighbors of the agents can be classified as cooperative or noncooperative by introducing a cooperation-competition network into the modeling of the communication graph. The agent’s goal is to optimize the total objective function of the cooperators. Since agents can only communicate with their neighbors, they are unable to obtain complete information about cooperators. The distributed optimization algorithm is proposed to classify cooperative subnetworks by introducing additional auxiliary variables, and the outputs of all agents exponentially converge to the optimal solution of the optimization problem under the condition of satisfying the global equality constraint of the subnetwork. The Lyapunov stability theory is used to analyze the algorithm’s convergence. Simulation results show the effectiveness of the proposed algorithm in two examples of economic dispatch in smart grids and optimal area coverage in multi-sensor networks.